settings.outformat = "pdf";
unitsize(4cm);
real xmin = -0.1;
real xmax = 2;
real ymin = -0.1;
real ymax = 2;
path s = (0, 0){up}..(1, 1)..(xmax, sqrt(xmax));
fill(s--(xmax, 0)-- cycle, mediumgray);
draw(s);
arrowbar axisarrow = Arrow(TeXHead);
draw((xmin, 0)--(xmax, 0), arrow = axisarrow);
draw((0, ymin)--(0, ymax), arrow = axisarrow);
real x = 1.4;
real dx = .05;
path striptop = subpath(s, x, x + dx);
draw((x, 0)-- striptop--(x + dx, 0)-- cycle, blue);
clip(box((1, ymin), (1.6, 1.5)));